"Albion have tonight completed the signing of àanelkaofficiel on a one-year deal, with a further year's option in the club's favour," said a statement on the Premier League club's Twitter feed.
West Brom manager Steve Clarke, who briefly worked with Anelka at Chelsea, said in a club statement: "We are missing a bit of firepower from last year - we're trying to put that right - and to kick off with the signing of Nicolas at the start of the summer is a great boost for everyone at the club.
"The sole focus at the club is trying to build on what we did last season. "The more quality players you can bring to the club the better -- and no-one can question Nicolas' quality. "He's a player I have worked with before as I was at Chelsea when they signed him.
"He's got a great work ethic, looks after himself and is a consummate professional. "If you add that to the obvious talent he's got I think he can prove to be a really top signing for the club. "His experience with some of the top clubs in England and Europe will stand the group in good stead.
"Hopefully he will be able to inspire the other players to even greater heights than we managed to achieve last year."
The Baggies are Anelka's sixth Premier League team after he turned out for Arsenal, Manchester City, Bolton and Chelsea and had a loan spell at Liverpool.
Anelka signed for Chinese side Shanghai Shenhua at the start of last season but finished the campaign back in Europe with Italian giants Juventus.
He has also played for Paris St Germain, Real Madrid and Fenerbahce and won 69 caps for Framce scoring 14 goals. However, he has not played for Les Bleus since the 2010 World Cup.